Find the Slope of a Parallel Line 3x+2y=-2

$3 x + 2 y = - 2$

Step 1

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Subtract $3 x$ from both sides of the equation.

$2 y = - 2 - 3 x$

Divide each term in $2 y = - 2 - 3 x$ by $2$ and simplify.

Divide each term in $2 y = - 2 - 3 x$ by $2$ .

$\frac{2 y}{2} = \frac{- 2}{2} + \frac{- 3 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 2}{2} + \frac{- 3 x}{2}$

Divide $y$ by $1$ .

$y = \frac{- 2}{2} + \frac{- 3 x}{2}$

Simplify the right side.

Simplify each term.

Divide $- 2$ by $2$ .

$y = - 1 + \frac{- 3 x}{2}$

Move the negative in front of the fraction.

$y = - 1 - \frac{3 x}{2}$

Write in $y = m x + b$ form.

Reorder $- 1$ and $- \frac{3 x}{2}$ .

$y = - \frac{3 x}{2} - 1$

Reorder terms.

$y = - (\frac{3}{2} x) - 1$

Remove parentheses.

$y = - \frac{3}{2} x - 1$

Step 2

Using the slope-intercept form, the slope is $- \frac{3}{2}$ .

$m = - \frac{3}{2}$

Step 3

All lines that are parallel to $y = - \frac{3}{2} x - 1$ have the same slope of $- \frac{3}{2}$ .

$m_{parallel} = - \frac{3}{2}$

Step 4